As he was trying to sign up for health insurance through Kentucky's new online exchange this month, Kenny Wheeler hit a wall. Mr. Wheeler, an independent sales representative with a neuromuscular disorder, had succeeded where many in other states had failed, getting through a thicket of log-in pages. But when he tried to find out whether two health plans he liked would pay for his medications or let him keep his current doctors, he could not. He called one doctor on the spot, but the receptionist could not tell him whether the practice was in the new plan networks.